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Abstract

Recently, there has been significant research investigating new optical technologies for dimensional metrology of features 22 nm in critical dimension and smaller. When modeling optical measurements, a library of curves is assembled through the simulation of a multidimensional parameter space. A nonlinear regression routine described in this paper is then used to identify an optimum set of parameters that yields the closest experiment-to-theory agreement. However, parametric correlation, measurement noise, and model inaccuracy all lead to measurement uncertainty in the fitting process for optical critical dimension measurements. To improve the optical measurements, other techniques such as atomic force microscopy and scanning electronic microscopy can also be used to provide supplemental a priori information. In this paper, a Bayesian statistical approach is proposed to allow the combination of different measurement techniques that are based on different physical measurements. The effect of this hybrid metrology approach will be shown to reduce the uncertainties of the parameter estimators.

References

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Table 1.

Parametric OCD Fits to the Data in Fig. 2 Before and After the Inclusion of Data from AFM a

OCD Only a^k#(σa^k#)

AFM Only ak*(σak*)

Combined OCD and AFM With top, mid, height a^k#(σa^k#)

Top (nm)

33.7 (10.8)

37.6 (0.9)

38.0 (0.9)

Middle (nm)

48.9 (6.0)

48.0 (1.9)

48.9 (1.8)

Bottom (nm)

68.9 (8.3)

52.8 (3.3)

66.6 (2.7)

Height (nm)

60.0 (2.2)

57.5(0.7)*

58.6 (0.4)

n (% of nominal)

98.0 (1.0)

98.5 (0.5)

a The five adjustable OCD parameters are top width, middle width, bottom linewidth, line height, and the percent variation of the optical constant n. As discussed in the text, the bottom width (in italics) as reported is not used in the Bayesian analysis. A 2 nm oxide layer, shown in Fig. 1(a), on the polysilicon substrate is added to the measured AFM value, yielding a modified AFM height (*) that with the top and middle widths are embedded into the OCD regression.

Table 2.

Parametric OCD Fits to the Data in Fig. 3 Before and After the Inclusion of Data from an AFM a

OCD Only a^k#(σa^k#)

AFM Only ak*(σak*)

Combined OCD and AFM With top, mid, height a^k#(σa^k#)

Middle (nm)

35.6 (0.4)

35.3 (1.2)

35.2 (0.2)

SWA (°)

83.9 (0.7)

79.0 (0.7)

84.4 (0.6)

Height (nm)

69.6 (3.0)

73.1 (0.9)

72.9 (0.8)

a The three parameters are as defined in Fig. 1(b). The two length AFM values (total height and total width) are incorporated into the OCD regression using the Bayesian approach, as the AFM sidewall (in italics) is significantly different from the initial OCD result. Implications of this discrepancy are addressed in the text.

Tables (2)

Table 1.

Parametric OCD Fits to the Data in Fig. 2 Before and After the Inclusion of Data from AFM a

OCD Only a^k#(σa^k#)

AFM Only ak*(σak*)

Combined OCD and AFM With top, mid, height a^k#(σa^k#)

Top (nm)

33.7 (10.8)

37.6 (0.9)

38.0 (0.9)

Middle (nm)

48.9 (6.0)

48.0 (1.9)

48.9 (1.8)

Bottom (nm)

68.9 (8.3)

52.8 (3.3)

66.6 (2.7)

Height (nm)

60.0 (2.2)

57.5(0.7)*

58.6 (0.4)

n (% of nominal)

98.0 (1.0)

98.5 (0.5)

a The five adjustable OCD parameters are top width, middle width, bottom linewidth, line height, and the percent variation of the optical constant n. As discussed in the text, the bottom width (in italics) as reported is not used in the Bayesian analysis. A 2 nm oxide layer, shown in Fig. 1(a), on the polysilicon substrate is added to the measured AFM value, yielding a modified AFM height (*) that with the top and middle widths are embedded into the OCD regression.

Table 2.

Parametric OCD Fits to the Data in Fig. 3 Before and After the Inclusion of Data from an AFM a

OCD Only a^k#(σa^k#)

AFM Only ak*(σak*)

Combined OCD and AFM With top, mid, height a^k#(σa^k#)

Middle (nm)

35.6 (0.4)

35.3 (1.2)

35.2 (0.2)

SWA (°)

83.9 (0.7)

79.0 (0.7)

84.4 (0.6)

Height (nm)

69.6 (3.0)

73.1 (0.9)

72.9 (0.8)

a The three parameters are as defined in Fig. 1(b). The two length AFM values (total height and total width) are incorporated into the OCD regression using the Bayesian approach, as the AFM sidewall (in italics) is significantly different from the initial OCD result. Implications of this discrepancy are addressed in the text.